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Section 1.1 : Integer Exponents

9. Simplify the following expression and write the answer with only positive exponents.

\[{\left( {\frac{{{z^2}{y^{ - 1}}{x^{ - 3}}}}{{{x^{ - 8}}{z^6}{y^4}}}} \right)^{ - 4}}\] Show Solution

There is not really a whole lot to this problem. All we need to do is use the properties from this section to do the simplification.

\[{\left( {\frac{{{z^2}{y^{ - 1}}{x^{ - 3}}}}{{{x^{ - 8}}{z^6}{y^4}}}} \right)^{ - 4}} = {\left( {\frac{{{z^2}{x^8}}}{{{x^3}{z^6}{y^1}{y^4}}}} \right)^{ - 4}} = {\left( {\frac{{{x^5}}}{{{z^4}{y^5}}}} \right)^{ - 4}} = {\left( {\frac{{{z^4}{y^5}}}{{{x^5}}}} \right)^4} = \require{bbox} \bbox[2pt,border:1px solid black]{{\frac{{{z^{16}}{y^{20}}}}{{{x^{20}}}}}}\]

In this case since there was a fair amount of simplification that could be done on the fraction inside the parenthesis so we decided to do that simplification prior to dealing with the exponent on the parenthesis.